measures the shortfall in future performance caused by selecting an arm \(I_T^+\)  with only the incomplete information about \(\theta \)  accrued after \(T\)  measurements. We call \(\Delta _T\)  the simple regret at time \(T\) , after [1]}. Having in mind policy decisions where \(\mu (\theta , i,x)\)  denotes the utility generated for an individual with feature \(x\) , [2]} call this the utilitarian regret. The goal in the problem, informally, is to experiment intelligently so that simple regret is small after using as few measurements as possible. This objective can be formalized in two different ways in Propositions REF  and REF , allowing us to give insight into different aspects of the performance of DTS..
